Multiple choice

Directions: You are given two quantities, Quantity I and Quantity II. Compare the two quantities and choose the correct option accordingly. A can finish a work in 24 days, B in 9 days and C in 12 days. They work together for 3 days. Quantity I. Time taken by A and C to do the remaining work Quantity II. Time taken by B and C to do the remaining work

  1. Quantity I > Quantity II

  2. Quantity I < Quantity II

  3. Quantity I = Quantity II

  4. No relation
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A=1/24, B=1/9, C=1/12. Combined rate = 1/24 + 1/9 + 1/12 = (3+8+6)/72 = 17/72. In 3 days, they do 3 * 17/72 = 17/24. Remaining = 7/24. Q1: Time for A and C = (7/24) / (1/24 + 1/12) = (7/24) / (3/24) = 7/3 = 2.33 days. Q2: Time for B and C = (7/24) / (1/9 + 1/12) = (7/24) / (7/36) = (7/24) * (36/7) = 1.5 days. Q1 > Q2.

AI explanation

Let the total work be the least common multiple of 24, 9, and 12, which is 72 units. A's efficiency is 3 units per day, B's is 8 units per day, and C's is 6 units per day. Working together for 3 days, they complete 3 times 17 units per day, leaving 72 minus 51, or 21 units of work. For Quantity I, A and C take 21 divided by their combined efficiency of 9, which is 2.33 days; for Quantity II, B and C take 21 divided by their combined efficiency of 14, which is 1.5 days. Therefore, Quantity I is greater than Quantity II.

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